Problem: Rewrite as a simplified fraction. ${0.6\overline{7} = {?}}$
Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{aligned}100x &= 67.7777...\\ 10x &= 6.7777...\end{aligned}}$ Subtracting the two equations, we have: ${90x = 61}$ ${x = \dfrac{61}{90}} $